The invention relates to a gas bag for vehicles, having a flat, two-dimensional shape when being in an uninflated, vented condition and in a three-dimensional shape in an inflated condition. The invention relates in particular to a gas bag module with a gas bag which can be mounted at the roof of the vehicle and which, in an inflated condition, is arranged forward of a vehicle occupant, in particular between the windshield and the dashboard on the one hand and the vehicle occupant on the other hand. Gas bags which in an uninflated, vented condition have a two-dimensional shape offer advantages as regards their production. As the gas bag can be spread in a single plane, all fabric pieces from which the gas bag is made can be sewn together by using two-dimensional seams. These seams can simply be made when the pieces of the gas bag are spread out on a table.